In a medium bowl, combine the flour, baking powder, baking soda, salt, mixed spice, and cinnamon. Set aside.
In a small saucepan, melt 75g of butter over low heat. Pour into a large bowl.
Add the brown sugar, granulated sugar, and vanilla. Whisk to combine.
Beat in the eggs, one at a time, whisking well after each addition.
Add the dry ingredients and mix until the batter is smooth.
Grate the apples. Fold them into the batter until no traces of flour remain.
Pour the batter into a cake pan. Bake in the oven until a knife inserted in the center comes out clean.
Let cool 10 minutes in the pan, then turn out onto a wire rack. Turn the cake over to obtain a flat surface. Caramel Glaze: In the same pan, melt 40g of butter over medium heat. Add the heavy cream, a pinch of salt, and the brown sugar. Bring to a boil, stirring constantly, until the mixture thickens slightly and the sugar is dissolved. Immediately pour the glaze over the cake and spread with a spatula.